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A227501 Number of non-congruent solutions of x^2 - xy + y^2 == 1 (mod n). 0
1, 3, 6, 6, 6, 18, 6, 12, 18, 18, 12, 36, 12, 18, 36, 24, 18, 54, 18, 36, 36, 36, 24, 72, 30, 36, 54, 36, 30, 108, 30, 48, 72, 54, 36, 108, 36, 54, 72, 72, 42, 108, 42, 72, 108, 72, 48, 144, 42, 90, 108, 72, 54, 162, 72, 72, 108, 90, 60, 216, 60, 90, 108, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative: If p==2 (mod 3) then a(p^s)=(p+1)p^(s-1);If p==1 (mod 3) then a(p^s)=(p-1)p^(s-1); a(3^s)=2*3^s.

LINKS

Table of n, a(n) for n=1..64.

MATHEMATICA

Eisenstein[1] = 1; Eisenstein[n_] := Length@Select[Flatten[Table[{a, b}, {a, n}, {b, n}], 1], Mod[#[[1]]^2 + #[[2]]^2 - #[[1]]*#[[2]], n] == 1 &]; Array[Eisenstein, 100]

CROSSREFS

Sequence in context: A081289 A160504 A291801 * A294981 A079093 A153035

Adjacent sequences:  A227498 A227499 A227500 * A227502 A227503 A227504

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Jul 13 2013

STATUS

approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)